20090915, 22:12  #45 
"Phil"
Sep 2002
Tracktown, U.S.A.
3·373 Posts 
New sieve file just uploaded
Well now there are 309,722 candidates left in the sieve file. We just uploaded a new one, almost 1.85% smaller, mainly due to the removal of everything with factors between 200 trillion and 350 trillion. Actually, that only accounts for 1.67% smaller, I had also forgotten to remove the candidates with factors between 180 trillion and 190 trillion in the previous file. Thanks Geoff and Kent, and a big thank you to Lennart Vogel, who took some time out of his PrimeGrid work to do a big chunk of sieving for us! The three of you have together eliminated about 1 out of every 60 remaining candidates.
The new file will not speed up the sieving significantly, but it will reduce the number of factors reported on already eliminated numbers (by about 1.85%). I think our sieving status is much better now, I would think that we should be somewhere between 400 and 500 trillion at this point, and we will be at 400T before too long. The question of optimum sieve level is tricky. Every hour of sieving effort eventually saves much more time in PRP work, but not right away. At our current sieve level, I estimate that an hour of sieving work will save an hour of PRP work on average by time the exponents get up to around 7 to 8 million or so (depending upon whether you are doing 64bit or 32bit sieving.) If we expect at least one of these two sequences to survive to a high value of n, we eventually should sieve much deeper. Seventeen or Bust is doing their sieving work jointly with the Prime Sierpinski Project through PrimeGrid, which has the advantage of mobilizing large numbers of computers. We might eventually go the same route, but I am comfortable with this being a small project for now. What do the rest of you think? Also, if anyone has benchmarks for the new sieve file, I would appreciate hearing of them. Last fiddled with by philmoore on 20090915 at 22:13 
20090917, 03:34  #46 
Mar 2003
New Zealand
13·89 Posts 
Even though k=2131 was the lightest weight sequence (accounting for 30% of terms in the sieve), it contributed 24 (42%) of the 57 subsequences sieved by sr2sieve (i.e. there were 24 different values for n mod 720 for the sequence 2^n+2131).
So removing k=2131 from the sieve would be expected to increase speed by a factor of about sqrt(57/33) or 31% (for the BSGS step only, which normally accounts for the bulk of the total sieve time). With sr2sieve 1.8.9 on my Core 2 Duo 2.66GHz in 64/32 bit mode I was getting 5.04M/2.79M p/s with the old 3k file, and now 6.85M/3.73M p/s with the new 2k file, so about 36%/33% faster. 
20090917, 03:39  #47 
Mar 2003
New Zealand
13×89 Posts 
sr2sieve version 1.8.11 should be faster for this project. On my Core 2 Duo 2.66GHz in 64/32 bit mode I now get 7.27M/4.06M p/s with the current 2k sieve file, compared to 6.85M/3.73M p/s with version 1.8.9.

20090917, 03:52  #48 
"Phil"
Sep 2002
Tracktown, U.S.A.
3·373 Posts 
This is a significant increase in speed! Sievers, you might want to upgrade to 1.8.11 if you haven't already.

20090918, 02:12  #49 
Feb 2008
13_{8} Posts 
Thanks for the update Geoff! I've switched over and noticed a nice speed boost.

20091013, 19:14  #50 
"Phil"
Sep 2002
Tracktown, U.S.A.
3·373 Posts 
I now have 306,424 candidates left in the range 2M50M, a decrease of 3298 since September 15th when our sieving was at 350M. I will go ahead and upload a new sieve file, 1.06% smaller, later today.

20091125, 03:04  #51 
Mar 2003
New Zealand
13×89 Posts 
Now that there is just one squence left in the sieve, it seems that sr2sieve is once again not selecting the best parameters automatically, so please try adding "Q 720" to the command line to see if it is faster. e.g. to sieve the range 500T501T:
sr2sieve zz i dual_s.abcd p 500e12 P 501e12 Q 720 I have only tried it on a 32bit machine so far, but it looks like sr2sieve version 1.8.11 with the "Q 720" option is about 95% as fast as sr1sieve would be. (I tested sr1sieve on the sequence 40291*2^n+1 to compare with sr2sieve on the sequence 2^n+40291). It also looks like the sieving speed has almost doubled compared to sieving two sequences. I will do some more careful timings later. 
20091125, 03:12  #52 
Feb 2008
11 Posts 
Thanks Geoff for the tip. The Q 720 parameter gave me another speed boost. I about doubled in speed with the drop to just one n. I'm running about 11.5 million p/sec on my Q6600 on 64bit, before I was running about 6.4 million.

20091125, 17:18  #53 
Feb 2009
3·13 Posts 
Awesome. On my T6500, 64bit I went from 9.56M p/sec to 10.30M p/sec, so about 7.7% faster. Dropped my ETA by almost a day!
Last fiddled with by enderak on 20091125 at 17:20 
20091209, 01:37  #54 
Mar 2003
New Zealand
1157_{10} Posts 
These are the current per core sieving rates I am getting on my 2.66GHz Core 2 Duo:
32bit: 7.6M p/s (1T in 36.5 hr) 64bit: 13.3M p/s (1T in 20.9 hr) The 64bit executable will start to slow down as the sieving depth approaches 2^51 (about 2252T) due to the need to correct SSE2 rounding errors. Once depth reaches 2^51 the code will switch over to using the x87 FPU. When this happens the rates will be: 32bit: 7.7M p/s (1T in 36.1 hr) 64bit: 12.2M p/s (1T in 22.8 hr) The speed should then only increase very slowly (if at all) as the sieve depth increases. 
20100127, 02:32  #55 
Jun 2008
Wollongong, .au
3×61 Posts 
Congratulations to the Sieving team! The project just passed 1000T, which is an incredible effort!
Phil, if you have the original dual_s.abcd file lurking around, perhaps you could tell us just how big an effort this was? How many tests have been saved since the project went public? Edit: I have the .abcd file from my sieving at 5T, and there were 195061 lines for +40291. There are now 152364 lines. That's a 22% reduction, which is very impressive. Well done! Last fiddled with by paleseptember on 20100127 at 02:47 
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